DQN card game - how to represent the actions?
Because your action space is not discrete, It would not be wise to evaluate possible actions. What would probably be better is evaluating next states. This means evaluating the value of the state after the action with your neural network instead of the value of a action. 

Why is this better? 
You can use the neural net for each possible action , instead of trying to make the neural network figure out which actions are possible. the result would be taking the action of which the next state has the most value.